How would you make 100 mL of a carbonic acid buffer at 0.2 M and pH = 9.8 using 0.5 M HCO3 and either 0.1 M NaOH or 0.1 M HCl and water?
You want 100 mL of 0.2M so weigh out 0.2 mol NaHCO3, dissolve in some water, add 0.1M NaOH dropwise until the pH is 9.8. Transfer quantitatively to a 100 mL volumetric flask and dilute to the mark. Mix thoroughtly.
To make a 100 mL carbonic acid buffer at 0.2 M and pH = 9.8 using 0.5 M HCO3 and either 0.1 M NaOH or 0.1 M HCl, follow these steps:
1. Determine the molar ratio of HCO3 to H2CO3 using the Henderson-Hasselbalch equation:
pH = pKa + log([HCO3-]/[H2CO3])
Rearranging the equation gives:
[HCO3-]/[H2CO3] = 10^(pH - pKa)
The pKa of carbonic acid (H2CO3) is 6.1, so:
[HCO3-]/[H2CO3] = 10^(9.8 - 6.1) = 794.328
2. Determine the required concentrations of HCO3 and H2CO3:
Let x be the concentration of HCO3- in M, and y be the concentration of H2CO3 in M.
From the molar ratio, we can write:
x/y = 794.328
Also, since the total buffer concentration is 0.2 M:
x + y = 0.2
Solve these two equations simultaneously to find the values of x and y.
3. Prepare the buffer solution using either 0.1 M NaOH or 0.1 M HCl:
Start by calculating the amount of HCO3- required:
mL of HCO3- = (0.5 M HCO3-)(volume of buffer solution in mL)/(x M HCO3-)
Next, calculate the amount of H2CO3 needed:
mL of H2CO3 = (y M H2CO3)(volume of buffer solution in mL)
Subtract the amount of HCO3- from the total volume of the buffer solution to determine the amount of water needed:
mL of water = volume of buffer solution in mL - mL of HCO3- - mL of H2CO3
For example, let's say the calculated values are:
x = 0.17 M HCO3-
y = 0.03 M H2CO3
If using 0.1 M NaOH for titration, add the following amounts:
- (0.17 M HCO3-)(100 mL)/(0.5 M HCO3-) = 34 mL of 0.5 M HCO3-
- (0.03 M H2CO3)(100 mL) = 3 mL of 0.5 M H2CO3
- (100 mL - 34 mL - 3 mL) = 63 mL of water
- Finally, add 3.6 mL of 0.1 M NaOH to adjust the pH to 9.8
If using 0.1 M HCl for titration, add the following amounts:
- (0.17 M HCO3-)(100 mL)/(0.5 M HCO3-) = 34 mL of 0.5 M HCO3-
- (0.03 M H2CO3)(100 mL) = 3 mL of 0.5 M H2CO3
- (100 mL - 34 mL - 3 mL) = 63 mL of water
- Finally, add 3.6 mL of 0.1 M HCl to adjust the pH to 9.8
Note: The volumes of 0.1 M NaOH or 0.1 M HCl mentioned are hypothetical values and may need adjustment based on the actual pH measurement.
To prepare a 100 mL carbonic acid buffer at 0.2 M with a pH of 9.8, we can use the Henderson-Hasselbalch equation:
pH = pKa + log([A-]/[HA])
In this case, carbonic acid (H2CO3) is the acid (HA) and bicarbonate ion (HCO3-) is the conjugate base (A-). The pKa value for carbonic acid is 6.37.
Step 1: Calculate the ratio of [A-] to [HA]
Using the Henderson-Hasselbalch equation, we can rearrange it to solve for the ratio [A-]/[HA]:
pH - pKa = log([A-]/[HA])
9.8 - 6.37 = log([A-]/[HA])
3.43 = log([A-]/[HA])
To convert this to a ratio, we need to take the antilog of both sides:
Antilog(3.43) = [A-]/[HA]
This gives us the ratio [A-]/[HA] ≈ 2222
Step 2: Calculate the concentration of the acid (HA)
We are given that the concentration of HCO3- is 0.5 M, which is equivalent to the concentration of HA (since H2CO3 dissociates to form HCO3-), so [HA] = 0.5 M.
Step 3: Calculate the concentration of the base (A-)
Since we have the ratio [A-]/[HA] ≈ 2222 and the concentration of HA is 0.5 M, we can calculate the concentration of A-:
[A-] = (2222)([HA])
[A-] = (2222)(0.5 M)
[A-] = 1111 M
Step 4: Prepare the buffer solution
We have two options for adjusting the pH: using either NaOH or HCl. Let's explore both options:
Option 1: Using NaOH
The reaction between HCO3- and NaOH forms H2O and NaHCO3, which does not significantly affect the concentration of HCO3- or H2CO3.
To prepare the buffer:
1. Measure 100 mL of 0.5 M HCO3- solution.
2. Calculate the amount of NaOH needed to adjust the pH. To do this, we need to calculate the difference between the final pH (9.8) and the pH of the starting solution (which we assume to be around 7):
Delta pH = Final pH - Starting pH
Delta pH = 9.8 - 7
Delta pH = 2.8
3. Calculate the amount (in moles) of NaOH needed to adjust the pH:
moles NaOH = Delta pH × volume (in L) × molarity
moles NaOH = 2.8 × 0.1 L × 0.1 M
moles NaOH = 0.028 moles
4. Add 0.028 moles of NaOH to the 0.5 M HCO3- solution while stirring until completely dissolved.
5. Adjust the volume to 100 mL using distilled water. This will give you a 100 mL carbonic acid buffer solution at 0.2 M with a pH of 9.8.
Option 2: Using HCl
The reaction between HCO3- and HCl forms H2O and CO2, which decreases the concentration of HCO3- and H2CO3. To adjust the pH, we will need to calculate the moles of HCl required to convert the desired amount of HCO3- into CO2 and water.
To prepare the buffer:
1. Measure 100 mL of 0.5 M HCO3- solution.
2. Calculate the amount of HCl needed to adjust the pH. Similar to the previous option, we calculate the difference in pH:
Delta pH = Final pH - Starting pH
Delta pH = 9.8 - 7
Delta pH = 2.8
3. Calculate the moles of HCO3- required to adjust the pH:
moles HCO3- = Delta pH × volume (in L) × molarity
moles HCO3- = 2.8 × 0.1 L × 0.5 M
moles HCO3- = 0.14 moles
4. Since the reaction between HCO3- and HCl is a 1:1 ratio, add 0.14 moles of HCl to the 0.5 M HCO3- solution while stirring until completely dissolved.
5. Adjust the volume to 100 mL using distilled water. This will result in a 100 mL carbonic acid buffer solution at 0.2 M with a pH of 9.8.
It is important to note that due to the nature of carbonic acid and its equilibrium with bicarbonate ions, the actual achieved pH may differ slightly from the expected value. Additionally, proper safety protocols should be followed when handling and diluting chemicals.